Normalized Solutions to Schrödinger Equations with General Nonlinearities in Bounded Domains via a Global Bifurcation Approach
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917776888692736 |
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| author | Ji, Wei |
| author_facet | Ji, Wei |
| contents | We obtain the existence, nonexistence and multiplicity of positive solutions with prescribed mass for nonlinear Schrödinger equations in bounded domains via a global bifurcation approach. The nonlinearities in this paper can be mass supercritical, critical, subcritical or some mixes of these cases, and the equation can be autonomous or non-autonomous. This generalizes a result in Noris, Tavares and Verzini [\emph{Anal. PDE}, 7 (8) (2014) 1807-1838], where the equation is autonomous with homogeneous nonlinearities. Besides, we have proven some orbital stability or instability results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_10299 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Normalized Solutions to Schrödinger Equations with General Nonlinearities in Bounded Domains via a Global Bifurcation Approach Ji, Wei Analysis of PDEs 35A15, 35B09, 35B40, 35B35 We obtain the existence, nonexistence and multiplicity of positive solutions with prescribed mass for nonlinear Schrödinger equations in bounded domains via a global bifurcation approach. The nonlinearities in this paper can be mass supercritical, critical, subcritical or some mixes of these cases, and the equation can be autonomous or non-autonomous. This generalizes a result in Noris, Tavares and Verzini [\emph{Anal. PDE}, 7 (8) (2014) 1807-1838], where the equation is autonomous with homogeneous nonlinearities. Besides, we have proven some orbital stability or instability results. |
| title | Normalized Solutions to Schrödinger Equations with General Nonlinearities in Bounded Domains via a Global Bifurcation Approach |
| topic | Analysis of PDEs 35A15, 35B09, 35B40, 35B35 |
| url | https://arxiv.org/abs/2409.10299 |